Two rods A and B of identical dimensions are at temperature $30^{0} C .$ If A is heated up to $180^{0} C$ and B is up to $T^{0} C,$ then their new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is $4 : 3,$ then the value of T is

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$230^{0} C$

$270^{0} C$

$250^{0} C$

$200^{0} C$

answer is B.

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Detailed Solution

$\begin{array}{l} Δ l_{1} = Δ l_{2}, l α_{1} Δ T_{1} = l α_{2} Δ T_{2} \\ \frac{α_{1}}{α_{2}} = \frac{Δ T_{2}}{Δ T_{1}}, \frac{4}{3} = \frac{T - 30}{180 - 30} \end{array}$

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